First Fundamental Theorem of Integrals
A(x) = b∫af(x)dx∫abf(x)dxfor all x ≥ a, where the function is continuous on [a,b]. Then A'(x) = f(x) for all x ϵ [a,b]
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Second Fundamental Theorem of Integrals
If f is continuous function of x defined on the closed interval [a,b] and F be another function such that d/dx F(x) = f(x) for all x in the domain of f, then b∫af(x)dx∫abf(x)dx = f(b) -f(a). This is known as the definite integralof f over the range [a,b], a being the lower limit and b the upper limit. Integral calculus is used for solving the probl
Indefinite Integrals
These are the integrals that do not have a pre-existing value of limits; thus making the final value of integral indefinite. ∫g'(x)dx = g(x) + c. Indefinite integrals belong to the family of parallel curves.
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Definite Integrals
The definite integrals have a pre-existing value of limits, thus making the final value of an integral, definite. if f(x) is a function of the curve, then b∫af(x)dx=f(b)−f(a)∫abf(x)dx=f(b)−f(a)
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